DESCRIPTION

Math::BigRat complements Math::BigInt and Math::BigFloat by providing
support for arbitrary big rational numbers.
MATHLIBRARY
You can change the underlying module that does the low-level math
operations by using:
use Math::BigRat try => 'GMP';
Note: This needs Math::BigInt::GMP installed.
The following would first try to find Math::BigInt::Foo, then
Math::BigInt::Bar, and when this also fails, revert to
Math::BigInt::Calc:
use Math::BigRat try => 'Foo,Math::BigInt::Bar';
If you want to get warned when the fallback occurs, replace "try" with
"lib":
use Math::BigRat lib => 'Foo,Math::BigInt::Bar';
If you want the code to die instead, replace "try" with "only":
use Math::BigRat only => 'Foo,Math::BigInt::Bar';

METHODS

Any methods not listed here are derived from Math::BigFloat (or
Math::BigInt), so make sure you check these two modules for further
information.
new()
$x = Math::BigRat->new('1/3');
Create a new Math::BigRat object. Input can come in various forms:
$x = Math::BigRat->new(123); # scalars
$x = Math::BigRat->new('inf'); # infinity
$x = Math::BigRat->new('123.3'); # float
$x = Math::BigRat->new('1/3'); # simple string
$x = Math::BigRat->new('1 / 3'); # spaced
$x = Math::BigRat->new('1 / 0.1'); # w/ floats
$x = Math::BigRat->new(Math::BigInt->new(3)); # BigInt
$x = Math::BigRat->new(Math::BigFloat->new('3.1')); # BigFloat
$x = Math::BigRat->new(Math::BigInt::Lite->new('2')); # BigLite
# You can also give D and N as different objects:
$x = Math::BigRat->new(
Math::BigInt->new(-123),
Math::BigInt->new(7),
); # => -123/7
numerator()
$n = $x->numerator();
Returns a copy of the numerator (the part above the line) as signed
BigInt.
denominator()
$d = $x->denominator();
Returns a copy of the denominator (the part under the line) as
positive BigInt.
parts()
($n, $d) = $x->parts();
Return a list consisting of (signed) numerator and (unsigned)
denominator as BigInts.
numify()
my $y = $x->numify();
Returns the object as a scalar. This will lose some data if the
object cannot be represented by a normal Perl scalar (integer or
float), so use as_int() or "as_float()" instead.
This routine is automatically used whenever a scalar is required:
my $x = Math::BigRat->new('3/1');
@array = (0, 1, 2, 3);
$y = $array[$x]; # set $y to 3
as_int()/as_number()
$x = Math::BigRat->new('13/7');
print $x->as_int(), "\n"; # '1'
Returns a copy of the object as BigInt, truncated to an integer.
"as_number()" is an alias for "as_int()".
as_float()
$x = Math::BigRat->new('13/7');
print $x->as_float(), "\n"; # '1'
$x = Math::BigRat->new('2/3');
print $x->as_float(5), "\n"; # '0.66667'
Returns a copy of the object as BigFloat, preserving the accuracy
as wanted, or the default of 40 digits.
This method was added in v0.22 of Math::BigRat (April 2008).
as_hex()
$x = Math::BigRat->new('13');
print $x->as_hex(), "\n"; # '0xd'
Returns the BigRat as hexadecimal string. Works only for integers.
as_bin()
$x = Math::BigRat->new('13');
print $x->as_bin(), "\n"; # '0x1101'
Returns the BigRat as binary string. Works only for integers.
as_oct()
$x = Math::BigRat->new('13');
print $x->as_oct(), "\n"; # '015'
Returns the BigRat as octal string. Works only for integers.
from_hex()
my $h = Math::BigRat->from_hex('0x10');
Create a BigRat from a hexadecimal number in string form.
from_oct()
my $o = Math::BigRat->from_oct('020');
Create a BigRat from an octal number in string form.
from_bin()
my $b = Math::BigRat->from_bin('0b10000000');
Create a BigRat from an binary number in string form.
bnan()
$x = Math::BigRat->bnan();
Creates a new BigRat object representing NaN (Not A Number). If
used on an object, it will set it to NaN:
$x->bnan();
bzero()
$x = Math::BigRat->bzero();
Creates a new BigRat object representing zero. If used on an
object, it will set it to zero:
$x->bzero();
binf()
$x = Math::BigRat->binf($sign);
Creates a new BigRat object representing infinity. The optional
argument is either '-' or '+', indicating whether you want infinity
or minus infinity. If used on an object, it will set it to
infinity:
$x->binf();
$x->binf('-');
bone()
$x = Math::BigRat->bone($sign);
Creates a new BigRat object representing one. The optional argument
is either '-' or '+', indicating whether you want one or minus one.
If used on an object, it will set it to one:
$x->bone(); # +1
$x->bone('-'); # -1
length()
$len = $x->length();
Return the length of $x in digits for integer values.
digit()
print Math::BigRat->new('123/1')->digit(1); # 1
print Math::BigRat->new('123/1')->digit(-1); # 3
Return the N'ths digit from X when X is an integer value.
bnorm()
$x->bnorm();
Reduce the number to the shortest form. This routine is called
automatically whenever it is needed.
bfac()
$x->bfac();
Calculates the factorial of $x. For instance:
print Math::BigRat->new('3/1')->bfac(), "\n"; # 1*2*3
print Math::BigRat->new('5/1')->bfac(), "\n"; # 1*2*3*4*5
Works currently only for integers.
bround()/round()/bfround()
Are not yet implemented.
bmod()
$x->bmod($y);
Returns $x modulo $y. When $x is finite, and $y is finite and non-
zero, the result is identical to the remainder after floored
division (F-division). If, in addition, both $x and $y are
integers, the result is identical to the result from Perl's %
operator.
bmodinv()
$x->bmodinv($mod); # modular multiplicative inverse
Returns the multiplicative inverse of $x modulo $mod. If
$y = $x -> copy() -> bmodinv($mod)
then $y is the number closest to zero, and with the same sign as
$mod, satisfying
($x * $y) % $mod = 1 % $mod
If $x and $y are non-zero, they must be relative primes, i.e.,
"bgcd($y, $mod)==1". '"NaN"' is returned when no modular
multiplicative inverse exists.
bmodpow()
$num->bmodpow($exp,$mod); # modular exponentiation
# ($num**$exp % $mod)
Returns the value of $num taken to the power $exp in the modulus
$mod using binary exponentiation. "bmodpow" is far superior to
writing
$num ** $exp % $mod
because it is much faster - it reduces internal variables into the
modulus whenever possible, so it operates on smaller numbers.
"bmodpow" also supports negative exponents.
bmodpow($num, -1, $mod)
is exactly equivalent to
bmodinv($num, $mod)
bneg()
$x->bneg();
Used to negate the object in-place.
is_one()
print "$x is 1\n" if $x->is_one();
Return true if $x is exactly one, otherwise false.
is_zero()
print "$x is 0\n" if $x->is_zero();
Return true if $x is exactly zero, otherwise false.
is_pos()/is_positive()
print "$x is >= 0\n" if $x->is_positive();
Return true if $x is positive (greater than or equal to zero),
otherwise false. Please note that '+inf' is also positive, while
'NaN' and '-inf' aren't.
"is_positive()" is an alias for "is_pos()".
is_neg()/is_negative()
print "$x is < 0\n" if $x->is_negative();
Return true if $x is negative (smaller than zero), otherwise false.
Please note that '-inf' is also negative, while 'NaN' and '+inf'
aren't.
"is_negative()" is an alias for "is_neg()".
is_int()
print "$x is an integer\n" if $x->is_int();
Return true if $x has a denominator of 1 (e.g. no fraction parts),
otherwise false. Please note that '-inf', 'inf' and 'NaN' aren't
integer.
is_odd()
print "$x is odd\n" if $x->is_odd();
Return true if $x is odd, otherwise false.
is_even()
print "$x is even\n" if $x->is_even();
Return true if $x is even, otherwise false.
bceil()
$x->bceil();
Set $x to the next bigger integer value (e.g. truncate the number
to integer and then increment it by one).
bfloor()
$x->bfloor();
Truncate $x to an integer value.
bint()
$x->bint();
Round $x towards zero.
bsqrt()
$x->bsqrt();
Calculate the square root of $x.
broot()
$x->broot($n);
Calculate the N'th root of $x.
badd()
$x->badd($y);
Adds $y to $x and returns the result.
bmul()
$x->bmul($y);
Multiplies $y to $x and returns the result.
bsub()
$x->bsub($y);
Subtracts $y from $x and returns the result.
bdiv()
$q = $x->bdiv($y);
($q, $r) = $x->bdiv($y);
In scalar context, divides $x by $y and returns the result. In list
context, does floored division (F-division), returning an integer
$q and a remainder $r so that $x = $q * $y + $r. The remainer
(modulo) is equal to what is returned by "$x-"bmod($y)>.
bdec()
$x->bdec();
Decrements $x by 1 and returns the result.
binc()
$x->binc();
Increments $x by 1 and returns the result.
copy()
my $z = $x->copy();
Makes a deep copy of the object.
Please see the documentation in Math::BigInt for further details.
bstr()/bsstr()
my $x = Math::BigRat->new('8/4');
print $x->bstr(), "\n"; # prints 1/2
print $x->bsstr(), "\n"; # prints 1/2
Return a string representing this object.
bcmp()
$x->bcmp($y);
Compares $x with $y and takes the sign into account. Returns -1,
0, 1 or undef.
bacmp()
$x->bacmp($y);
Compares $x with $y while ignoring their sign. Returns -1, 0, 1 or
undef.
beq()
$x -> beq($y);
Returns true if and only if $x is equal to $y, and false otherwise.
bne()
$x -> bne($y);
Returns true if and only if $x is not equal to $y, and false
otherwise.
blt()
$x -> blt($y);
Returns true if and only if $x is equal to $y, and false otherwise.
ble()
$x -> ble($y);
Returns true if and only if $x is less than or equal to $y, and
false otherwise.
bgt()
$x -> bgt($y);
Returns true if and only if $x is greater than $y, and false
otherwise.
bge()
$x -> bge($y);
Returns true if and only if $x is greater than or equal to $y, and
false otherwise.
blsft()/brsft()
Used to shift numbers left/right.
Please see the documentation in Math::BigInt for further details.
band()
$x->band($y); # bitwise and
bior()
$x->bior($y); # bitwise inclusive or
bxor()
$x->bxor($y); # bitwise exclusive or
bnot()
$x->bnot(); # bitwise not (two's complement)
bpow()
$x->bpow($y);
Compute $x ** $y.
Please see the documentation in Math::BigInt for further details.
blog()
$x->blog($base, $accuracy); # logarithm of x to the base $base
If $base is not defined, Euler's number (e) is used:
print $x->blog(undef, 100); # log(x) to 100 digits
bexp()
$x->bexp($accuracy); # calculate e ** X
Calculates two integers A and B so that A/B is equal to "e ** $x",
where "e" is Euler's number.
This method was added in v0.20 of Math::BigRat (May 2007).
See also "blog()".
bnok()
$x->bnok($y); # x over y (binomial coefficient n over k)
Calculates the binomial coefficient n over k, also called the
"choose" function. The result is equivalent to:
( n ) n!
| - | = -------
( k ) k!(n-k)!
This method was added in v0.20 of Math::BigRat (May 2007).
config()
use Data::Dumper;
print Dumper ( Math::BigRat->config() );
print Math::BigRat->config()->{lib}, "\n";
Returns a hash containing the configuration, e.g. the version
number, lib loaded etc. The following hash keys are currently
filled in with the appropriate information.
key RO/RW Description
Example
============================================================
lib RO Name of the Math library
Math::BigInt::Calc
lib_version RO Version of 'lib'
0.30
class RO The class of config you just called
Math::BigRat
version RO version number of the class you used
0.10
upgrade RW To which class numbers are upgraded
undef
downgrade RW To which class numbers are downgraded
undef
precision RW Global precision
undef
accuracy RW Global accuracy
undef
round_mode RW Global round mode
even
div_scale RW Fallback accuracy for div
40
trap_nan RW Trap creation of NaN (undef = no)
undef
trap_inf RW Trap creation of +inf/-inf (undef = no)
undef
By passing a reference to a hash you may set the configuration
values. This works only for values that a marked with a "RW" above,
anything else is read-only.

BUGS

Please report any bugs or feature requests to "bug-math-bigrat at
rt.cpan.org", or through the web interface at
<https://rt.cpan.org/Ticket/Create.html?Queue=Math-BigRat> (requires
login). We will be notified, and then you'll automatically be notified
of progress on your bug as I make changes.